{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2b3c1457-3e45-4573-8bb9-edd12151de6c",
   "metadata": {
    "panel-layout": {
     "height": 0,
     "visible": true,
     "width": 100
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "aaaaa\n"
     ]
    }
   ],
   "source": [
    "x = 5\n",
    "x = \"a\" * x\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f184af81-b153-4175-8def-109dc0296854",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "4a0d491d-c2de-47e4-9d60-e83d2989a489",
   "metadata": {
    "panel-layout": {
     "height": 114.5625,
     "visible": true,
     "width": 100
    }
   },
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4a080f55-67e7-4ed3-a00f-2a7c4c87b063",
   "metadata": {},
   "outputs": [],
   "source": [
    "import time\n",
    "\n",
    "while True:\n",
    "    print(\"hello\")\n",
    "    time.sleep(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41ffa1b4-06df-4b0b-8405-37947f6bb130",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "87558d84-7632-4427-a0f0-1e0644f028fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(\"done\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6e4336c0-525a-4b51-ac4c-2b7349ca9960",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c62a9e86-412f-4a83-9fbe-502692702bd0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "00"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b86ab929-f0e3-43fe-88c0-8f0dcbf0530c",
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'x' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[1], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m x\n",
      "\u001b[1;31mNameError\u001b[0m: name 'x' is not defined"
     ]
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d962cada-85a7-482f-8da2-bbeecff17558",
   "metadata": {},
   "source": [
    "x = 20"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "723faeef-1ecb-421f-95d1-ac3a52330dbb",
   "metadata": {},
   "source": [
    "# 一级标题\n",
    "\n",
    "## 二级标题\n",
    "\n",
    "### 三级标题\n",
    "\n",
    "#### 有序列表\n",
    "1. 第一项内容\n",
    "2. 第二项内容\n",
    "   - 嵌套的无序列表项1\n",
    "   - 嵌套的无序列表项2\n",
    "3. 第三项内容\n",
    "\n",
    "#### 无序列表\n",
    "- 项目A\n",
    "- 项目B\n",
    "  1. 嵌套的有序列表项1\n",
    "  2. 嵌套的有序列表项2\n",
    "- 项目C\n",
    "\n",
    "### 三级标题：引用与代码\n",
    "\n",
    "#### 引用示例\n",
    "> 这是一级引用\n",
    ">> 这是嵌套的二级引用\n",
    ">\n",
    "> 回到一级引用\n",
    "\n",
    "#### 代码展示\n",
    "行内代码：`print(\"Hello Markdown\")`\n",
    "\n",
    "代码块（带语言标识）：\n",
    "```python\n",
    "def greeting(name):\n",
    "    print(f\"Hello, {name}!\")\n",
    "\n",
    "greeting(\"World\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a65702a5-343f-4edf-95ab-1c81c7e52542",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## 🌟 基础文本格式\n",
    "- **加粗文本**：用于突出重点内容\n",
    "- *斜体文本*：适合强调或补充说明\n",
    "- ***加粗斜体文本***：双重强调效果\n",
    "- ~~删除线文本~~：表示已废弃或错误内容\n",
    "- `代码样式文本`：用于单行代码或变量名（如 `pd.DataFrame()`）\n",
    "\n",
    "## 📋 列表功能\n",
    "### 有序列表（步骤演示）\n",
    "1. 导入必要库（`import numpy as np`）\n",
    "2. 加载数据集\n",
    "3. 数据预处理\n",
    "   - 处理缺失值\n",
    "   - 特征标准化\n",
    "4. 模型训练与评估\n",
    "\n",
    "### 无序列表（要点列举）\n",
    "- 数据可视化工具\n",
    "  - Matplotlib（基础绘图）\n",
    "  - Seaborn（统计绘图）\n",
    "  - Plotly（交互式绘图）\n",
    "- 常用数据格式\n",
    "  - CSV\n",
    "  - JSON\n",
    "  - Excel\n",
    "\n",
    "### 任务列表\n",
    "- [x] 完成数据加载\n",
    "- [x] 绘制基础分布图\n",
    "- [ ] 优化图表样式\n",
    "- [ ] 撰写分析结论\n",
    "\n",
    "## 🧮 代码块与公式\n",
    "### 代码块示例（Python）\n",
    "```python\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 生成示例数据\n",
    "x = np.linspace(0, 2*np.pi, 100)\n",
    "y = np.sin(x)\n",
    "\n",
    "# 绘制图形\n",
    "plt.figure(figsize=(8, 4))\n",
    "plt.plot(x, y, label='sin(x)')\n",
    "plt.title('正弦函数曲线')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "```\n",
    "\n",
    "### 数学公式（LaTeX 支持）\n",
    "- 行内公式：正弦函数的导数是 $\\cos(x)$，即 $\\frac{d}{dx}\\sin(x) = \\cos(x)$\n",
    "- 块级公式：欧拉公式  \n",
    "  $$e^{i\\pi} + 1 = 0$$  \n",
    "  正态分布概率密度函数  \n",
    "  $$f(x) = \\frac{1}{\\sqrt{2\\pi}\\sigma} e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}$$\n",
    "\n",
    "## 📊 表格与图表\n",
    "### 数据对比表格\n",
    "| 模型名称 | 准确率 | 召回率 | F1分数 |\n",
    "|----------|--------|--------|--------|\n",
    "| 逻辑回归 | 0.85   | 0.82   | 0.83   |\n",
    "| 随机森林 | 0.91   | 0.89   | 0.90   |\n",
    "| SVM      | 0.88   | 0.86   | 0.87   |\n",
    "\n",
    "### 图片展示（支持本地/网络图片）\n",
    "#### 示例图片1：数据可视化示例\n",
    "![数据分布散点图](https://picsum.photos/id/180/800/400)  \n",
    "*图1：随机生成的散点图（实际使用时替换为本地图片路径或数据集可视化结果）*\n",
    "\n",
    "#### 示例图片2：Jupyter Notebook 界面\n",
    "![Jupyter Notebook 界面](https://picsum.photos/id/0/800/400)  \n",
    "*图2：Jupyter Notebook 工作界面示意图*\n",
    "\n",
    "## 🔗 链接与引用\n",
    "- [Jupyter 官方文档](https://jupyter.org/documentation)\n",
    "- [Markdown 语法指南](https://www.markdownguide.org)\n",
    "- 引用示例：  \n",
    "  > 数据科学的核心是从数据中提取有价值的见解 —— 《数据科学实战》\n",
    "\n",
    "## 📝 其他实用功能\n",
    "### 分割线\n",
    "---\n",
    "\n",
    "### 折叠块（配合 HTML，Jupyter 支持）\n",
    "<details>\n",
    "  <summary>点击展开：扩展知识点</summary>\n",
    "  - Jupyter Notebook 支持 Markdown 与代码块混合编辑\n",
    "  - 可通过 `%matplotlib inline` 命令设置图表内嵌显示\n",
    "  - 使用 `?函数名` 可快速查看函数文档\n",
    "</details>\n",
    "\n",
    "### 颜色标记（配合 HTML）\n",
    "<span style=\"color:red\">重要提示：</span> 运行大型数据集时建议使用 `dask` 或 `vaex` 库进行并行计算  \n",
    "<span style=\"color:green\">技巧：</span> 按 `Shift+Enter` 可快速运行单元格并跳至下一行\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "265cfb74-1a58-4f58-a910-cebcc6128f08",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\\begin{document}\n",
    "\n",
    "\\section{复杂数学公式示例}\n",
    "\n",
    "\\subsection{1. 微积分与微分方程}\n",
    "\n",
    "% 纳维-斯托克斯方程（流体力学核心方程）\n",
    "\\begin{equation}\n",
    "\\rho \\left( \\frac{\\partial \\mathbf{u}}{\\partial t} + \\mathbf{u} \\cdot \\nabla \\mathbf{u} \\right) \n",
    "= -\\nabla p + \\mu \\nabla^2 \\mathbf{u} + \\rho \\mathbf{g}\n",
    "\\end{equation}\n",
    "其中，$\\rho$ 为流体密度，$\\mathbf{u}$ 为速度矢量，$p$ 为压强，$\\mu$ 为动力黏度，$\\mathbf{g}$ 为重力加速度。\n",
    "\n",
    "\n",
    "\\subsection{2. 线性代数与矩阵论}\n",
    "\n",
    "% 广义特征值问题与矩阵束\n",
    "\\begin{equation}\n",
    "\\det(A - \\lambda B) = 0\n",
    "\\end{equation}\n",
    "对于一对 $n \\times n$ 矩阵 $(A, B)$，上式的解 $\\lambda$ 称为广义特征值，对应的非零向量 $\\mathbf{x}$ 满足：\n",
    "\\begin{equation}\n",
    "(A - \\lambda B)\\mathbf{x} = \\mathbf{0}\n",
    "\\end{equation}\n",
    "\n",
    "% 矩阵指数函数（含收敛条件）\n",
    "\\begin{equation}\n",
    "e^{\\mathbf{A}} = \\sum_{k=0}^{\\infty} \\frac{\\mathbf{A}^k}{k!} \n",
    "\\quad \\text{其中 } \\left\\| \\mathbf{A}^k \\right\\| \\leq \\frac{M r^k}{k!} \\to 0 \\, (k \\to \\infty)\n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "\\subsection{3. 概率论与随机过程}\n",
    "\n",
    "% 维纳过程的转移概率密度\n",
    "设 $W(t)$ 为标准维纳过程，则其转移概率密度满足：\n",
    "\\begin{equation}\n",
    "p(w, t \\mid w_0, 0) = \\frac{1}{\\sqrt{2\\pi t}} \n",
    "\\exp\\left( -\\frac{(w - w_0)^2}{2t} \\right)\n",
    "\\quad (t > 0, w, w_0 \\in \\mathbb{R})\n",
    "\\end{equation}\n",
    "\n",
    "% 随机微分方程（伊藤形式）\n",
    "对于半鞅 $X_t$ 和可测过程 $\\mu_t, \\sigma_t$，伊藤随机微分方程为：\n",
    "\\begin{equation}\n",
    "dX_t = \\mu_t(X_t) dt + \\sigma_t(X_t) dW_t\n",
    "\\quad \\text{其中 } \\int_0^T |\\mu_t| dt < \\infty, \\int_0^T \\sigma_t^2 dt < \\infty \\, \\text{a.s.}\n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "\\subsection{4. 量子力学与场论}\n",
    "\n",
    "% 狄拉克方程（相对论量子力学）\n",
    "\\begin{equation}\n",
    "(i\\gamma^\\mu \\partial_\\mu - m)\\psi = 0\n",
    "\\end{equation}\n",
    "其中 $\\gamma^\\mu$ 为狄拉克矩阵，满足 $\\{\\gamma^\\mu, \\gamma^\\nu\\} = 2g^{\\mu\\nu}\\mathbf{1}$，$\\psi$ 为旋量场。\n",
    "\n",
    "% 费曼路径积分（量子振幅）\n",
    "\\begin{equation}\n",
    "\\langle q_f, t_f \\mid q_i, t_i \\rangle \n",
    "= \\int \\mathcal{D}[q(t)] \\exp\\left( \\frac{i}{\\hbar} S[q(t)] \\right)\n",
    "\\end{equation}\n",
    "$S[q(t)] = \\int_{t_i}^{t_f} L(q, \\dot{q}, t) dt$ 为作用量泛函，$\\mathcal{D}[q(t)]$ 为路径测度。\n",
    "\n",
    "\n",
    "\\subsection{5. 特殊函数与积分变换}\n",
    "\n",
    "% 超几何函数（级数定义）\n",
    "\\begin{equation}\n",
    "{}_2F_1(a, b; c; z) = \\sum_{n=0}^{\\infty} \\frac{(a)_n (b)_n}{(c)_n n!} z^n\n",
    "\\quad (|z| < 1, c \\notin \\mathbb{Z}_{\\leq 0})\n",
    "\\end{equation}\n",
    "其中 $(x)_n = x(x+1)\\cdots(x+n-1)$ 为波沙克符号（Pochhammer symbol）。\n",
    "\n",
    "% 梅林变换（与傅里叶变换的关系）\n",
    "函数 $f(x)$ 的梅林变换定义为：\n",
    "\\begin{equation}\n",
    "\\mathcal{M}\\{f\\}(s) = \\int_0^\\infty x^{s-1} f(x) dx\n",
    "\\end{equation}\n",
    "其与傅里叶变换的关系为：$\\mathcal{M}\\{f\\}(s) = \\mathcal{F}\\{f(e^{-t})\\}(is)$。\n",
    "\n",
    "\n",
    "\\end{document}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c94e5e77-9bb8-4857-81e1-f597e72ef053",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  },
  "panel-cell-order": [
   "2b3c1457-3e45-4573-8bb9-edd12151de6c",
   "4a0d491d-c2de-47e4-9d60-e83d2989a489"
  ]
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
